1 Answers

Best Answer

f(x,y)=ysin^(-1)xy
Differentiate with respect to y, treat x like a constants
f_(y)(x,y)=sin^(-1)xy+y*(1)/(sqrt(1-x^(2)y^(2)))*x
f_(y)(x,y)=sin^(-1)xy+(xy)/(sqrt(1-x^(2)y^(2)))
Therefore
f_(y)(1, (1)/(2))=sin^(-1)(1)/(2)+((1)/(2))/(sqrt(1-(1)/(4)))
f_(y)(1,(1)/(2))=(pi)/(6)+((1)/(2))/((sqrt(3))/(2))
f_(y)(1,(1)/(2))=(pi)/(6)+(1)/(sqrt(3))
Result:
f_(y)(1,(1)/(2))=(pi)/(6)+(1)/(sqrt(3))